We present a system for keyframe-based dense camera tracking and depth map estimation that is entirely learned. For tracking, we estimate small pose increments between the current camera image and a synthetic viewpoint based on the color and depth image of a keyframe. It significantly simplifies the learning problem and alleviates the dataset bias for camera motions. Further, we show that generating a large number of pose hypotheses leads to more accurate predictions. For mapping, we accumulate information in a cost volume centered at the current depth estimate. The mapping network then combines the cost volume and the keyframe image to update the depth prediction, thereby effectively making use of depth measurements and image-based priors. Our approach yields state-of-the-art results with few images and is robust with respect to noisy camera poses. We demonstrate that the performance of our 6 DOF tracking competes with RGB-D tracking algorithms.We compare favorably against strong classic and deep learning powered dense depth algorithms.